Physics
Physics
5th Edition
ISBN: 9781260487008
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 9, Problem 49P

(a)

To determine

The speed of water in the hose.

(a)

Expert Solution
Check Mark

Answer to Problem 49P

The speed of water in the hose is v2=39.1cm/s_.

Explanation of Solution

Write the continuity equation

ΔVΔt=A1v1=A2v2 (I)

Here, ΔVΔt is the volume flow rate, A1 and A2 is inner and outer area, v1 and v2 are velocities

Write continuity equation in case hose and obtain expression of v2 using equation (I)

A1v1=A2v2v2=A1A2v1 (II)

Replace A1 and A2 by πr12, and πr22 respectively in equation (II)

v2=πr12πr22v1=r12r22v1 (III)

Conclusion:

Substitute 1.00mm for r1, 8.00mm for r2, and 25.0m/s  for v1 in equation (III)

v2=(1.00mm)2(8.00mm)2(25.0m/s )=39.1cm/s

Therefore, the speed of water in the hose is v2=39.1cm/s_.

(b)

To determine

The volume flow rate.

(b)

Expert Solution
Check Mark

Answer to Problem 49P

The volume flow rate is ΔVΔt=78.5cm3/s_.

Explanation of Solution

From equation (I) in part (A) the expression for volume flow rate is

ΔVΔt=A1v1=πr12v1 (IV)

Conclusion:

Substitute, 25m/s for v, 1.0mm for r in equation (IV)

ΔVΔt=3.14(1.0mm×101cm1mm)2(25m/s×102cm1m)=78.5cm3/s

Therefore, the volume flow rate is ΔVΔt=78.5cm3/s_.

(c)

To determine

The mass flow rate.

(c)

Expert Solution
Check Mark

Answer to Problem 49P

The mass flow rate ΔmΔt=78.5g/s_.

Explanation of Solution

Write the expression for mass flow rate

ΔmΔt=ρA1v1 (VI)

Here, ρ is the density, A1 is the area, v1 is the velocity

Conclusion:

Substitute, 1.0g/cm3 for ρ, 78.5cm3/s for A1v1, in equation (VI)

ΔmΔt=(1.0g/cm3)(78.5cm3/s)=78.5g/s

Therefore, the mass flow rate ΔmΔt=78.5g/s_.

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Chapter 9 Solutions

Physics

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